1). Prove that any sigma-algebra, which contains a finite number of members is also a topology. ( The Q in another words : to show that there exist a sequence of disjoint members of a sigma algebra which contains infinite no. of members).
2). Does there exist an infinite sigma-algebra which has only countably many members? (Of course justify, examples, anything needed to prove any claims made in the solution.)© BrainMass Inc. brainmass.com March 4, 2021, 6:31 pm ad1c9bdddf
We check the definition of sigma-algebra of topology. Suppose F is a sigma-algebra defined on the set X. We want to show that F is also a ...
Sigma-algebras are investigated. The solution is detailed and well presented.